Question

In the arrangement shown in figure above viscous liquid whose density is $\rho =1.0g/c{m}^3$ flows along a tube out of a wide tank $A$. Find the velocity (in m/s) of the liquid flow, if $h_1=10cm$, $h_2=20cm$, and $h_3=35cm$. All the distances $l$ are equal.

Answer 1

The loss of pressure head in travelling a distance $l$ is seen from
the middle section to be $h_2-h_1=10cm$. Since $h_2-h_1=h_1$ in
our problem and $h_3-h_2=15cm=5+h_2-h_1$, we see that a pressure
head of $5cm$ remains incompensated and must be converted into
kinetic energy, the liquid flow out. Thus
$\frac{\rho v^2}{2}=\rho g\Delta h$ where $\Delta h=h_3-h_2$
Thus $v=\sqrt{2g\Delta h}=1m/s$